Samoa School Syllabus - Mathematics

This syllabus outlines the curriculum for Mathematics and General Mathematics from Year 9 to Year 12. The structure is organized into strands, year levels, and tiers of learning outcomes. The overarching goal is to develop students' mathematical thinking, competence, and appreciation for the subject. The syllabus emphasizes practical application and problem-solving in various contexts. The two streams, Mathematics and General Mathematics, cater to different career pathways. Mathematics focuses on preparing students for science-related fields, while General Mathematics prepares students for TVET (Vocational) pathways.

Year 9 Mathematics (Common Curriculum)

This curriculum lays the foundation for both the Mathematics and General Mathematics pathways.

Working Mathematically

Students develop mathematical fluency through inquiry, strategic thinking, reasoning, reflection, and communication. They interpret questions, represent mathematical ideas, justify their reasoning, evaluate strategies, and communicate solutions.

Number & Operations

Students work with various number sets (integers, fractions, decimals, percentages), apply number properties, use scientific notation, and solve simple financial problems.

Algebra

Students develop algebraic techniques, work with indices, solve problems involving rates of change, and explore linear relationships. They learn to translate between words and algebraic symbols, solve linear equations and inequalities, and generate number patterns.

Statistics & Probability

Students explore chance events, develop probability language, calculate relative frequencies, and use 2-way tables. They also collect, display, and interpret data using measures of location and range.

Measurement

Students perform time calculations, convert metric measures, calculate perimeter and area using formulas and Pythagoras' Theorem, and explore surface area and volume. They also learn about limits of accuracy and scales.

Geometry

Students identify and classify angles, explore properties of geometrical figures, and work with transformations (translation, rotation, reflection). They also investigate circle properties and solve problems involving angle properties and polygons.

Trigonometry

Students apply trigonometry and Pythagoras' Theorem to solve problems involving right-angled triangles, including angles of elevation and depression. They also sketch graphs of sine and cosine functions.

Years 10-12 Mathematics (Science & Commerce Pathways)

This stream provides a more rigorous mathematical foundation for students pursuing science and commerce-related fields. The curriculum builds upon the Year 9 foundation and delves deeper into each strand.

Working Mathematically

The focus remains on developing the five interrelated processes of Working Mathematically: Interpreting & Posing Questions, Strategically Thinking & Representing, Reasoning & Justifying, Reflecting & Evaluating, and Communicating Mathematically.

Number & Operations

Students refine their understanding of number sets, work with surds and indices, and apply these concepts to rates and ratios. They learn to simplify surd expressions, use the Binomial Theorem, and solve complex problems involving rates and ratios.

Algebra

Students manipulate complex algebraic expressions, expand binomial products, factorize non-monic quadratic expressions, and solve various types of equations (quadratic, cubic, simultaneous, logarithmic). They also explore non-linear relationships and functions, including quadratics, cubics, exponentials, and circles.

Statistics & Probability

Students calculate probabilities using probability trees, analyze data using standard deviation, and investigate complex theoretical probabilities. They also delve deeper into data analysis, exploring skewed and symmetrical data sets, quartiles, interquartile range, mean, and standard deviation. Sampling methods and ethical considerations in data collection are also addressed.

Measurement

Students solve complex time problems, work with metric and imperial units, and calculate areas and volumes of complex shapes. They also explore limits of accuracy and work with scale drawings. Additionally, they are introduced to sequences and series, including arithmetic and geometric sequences.

Geometry

Students solve complex problems involving angle properties, parallel lines, and circle geometry. They also explore transformations in more depth, including enlargement and similarity.

Trigonometry

Students extend their knowledge of trigonometry to non-right-angled triangles, using the sine rule, cosine rule, and area rule. They also explore trigonometric functions and their graphs, including periodicity and symmetry. They investigate Pythagorean triads and solve complex problems involving trigonometric equations and identities.

Rates of Change & Calculus

Students explore rates of change, derivatives, and integrals. They learn about the relationship between a function and its derivative, and how integral calculus relates to area under curves. They also explore applications of differentiation, including maxima, minima, velocity, and acceleration.

Years 10-12 General Mathematics (TVET Pathway)

This stream focuses on practical applications of mathematics relevant to TVET careers.

Working Mathematically

Similar to the Mathematics stream, the emphasis is on developing the five processes of Working Mathematically.

Number & Operations

Students work with number sets, indices, and financial mathematics. They learn to graph number sets, perform operations with surds, and solve financial problems involving interest, budgeting, and taxes.

Algebra

Students simplify algebraic expressions, work with indices, and explore rates of change. They also work with linear and non-linear relationships, solve equations, and apply these concepts to practical problems.

Statistics & Probability

Students work with probability trees, theoretical probabilities, and data analysis. They learn to construct and interpret cumulative frequency tables, create graphs, and identify the process of statistical inquiry. Ethical considerations in data collection are also addressed.

Measurement

Students solve time problems, work with metric and imperial units, and calculate perimeter, area, surface area, and volume. They also explore limits of accuracy and interpret scales.

Geometry

Students work with angles, parallel lines, circles, and transformations. They solve problems involving angle properties, construct polygons, and explore geometric transformations.

Trigonometry

Students work with Pythagorean triads, trigonometric functions, and ratios. They apply these concepts to solve problems involving right-angled triangles and explore applications in 3D problems.

Rates of Change & Modelling Functions

Students explore rates of change and their relationship to graphs. They learn to derive equations to represent numerical patterns and use these to determine modelling functions for real-life situations. They also interpret straight-line graphs and explore limits of functions.